# Data for modular curve with label 12.64.1.b.1, downloaded from the LMFDB on 01 June 2024.
{"label": "12.64.1.b.1", "coarse_level": 12, "coarse_index": 64, "genus": 1, "coarse_label": "12.64.1.b.1", "coarse_class": "12.64.1.b", "coarse_class_num": 2, "coarse_num": 1, "level": 12, "index": 64, "fine_num": 0, "contains_negative_one": true, "determinant_label": "1.1.1", "scalar_label": "12.2.1", "generators": [[5, 8, 3, 11], [7, 1, 0, 1], [11, 8, 0, 7]], "canonical_generators": [[0, 1, 5, 4], [0, 1, 7, 9], [0, 1, 11, 1], [0, 11, 5, 3], [4, 5, 7, 9]], "parents": ["12.16.0.b.1", "12.32.1.b.1"], "parents_conj": [[1, 0, 0, 1], [1, 0, 0, 1]], "reductions": ["1.1.0.a.1", "3.4.0.a.1", "3.4.0.a.1", "4.8.0.b.1"], "factorization": [], "orbits": [[2, 3, 1], [3, 2, 1], [3, 6, 1], [4, 6, 2], [6, 6, 1], [6, 18, 1], [12, 6, 2], [12, 12, 1], [12, 36, 2]], "kummer_orbits": [[2, 3, 1], [3, 1, 1], [3, 3, 1], [4, 3, 2], [6, 3, 1], [6, 9, 1], [12, 3, 2], [12, 6, 1], [12, 18, 2]], "isogeny_orbits": [[2, 3, 1], [3, 1, 1], [3, 3, 1], [4, 3, 2], [6, 3, 1], [6, 9, 1], [12, 3, 2], [12, 9, 2]], "psl2index": 64, "nu2": 0, "nu3": 4, "cusps": 8, "psl2level": 12, "sl2level": 12, "rational_cusps": 2, "cusp_orbits": [[1, 2], [2, 3]], "cusp_widths": [[4, 4], [12, 4]], "psl2label": "12.64.1.a.1", "sl2label": "12.64.1.a.1", "CPlabel": "12R1", "Slabel": null, "SZlabel": null, "RZBlabel": null, "RSZBlabel": "12.64.1.24", "Glabel": "72.46", "name": null, "rank": 0, "genus_minus_rank": 1, "newforms": ["48.2.a.a"], "dims": [1], "mults": [1], "traces": [0, 1, -2, 0, -4, -2, 2, 4, 8, 6, -8, 6, -6, -4, 0, -2, -4, -2, 4, -8, 10, 8, 4, -6, 2, -18, -16, 12, -2, 18, 8, 4, -6, 12, 14, 16, -2, -12, -24, 6, -12, 6, 0, 2, -18, -16, 20, 8, -12, 22, 10, 16, 18, -20, 2, 8, -10, -8, -26, 26, 28, -18, -12, 24, -6, 6, -20, 18, 12, 30, 2, 24, 8, -10, -20, 0, -2, 14, -30, -6, -12, -10, -32, -14, 0, -20, -14, -22, -26, -8, 36, 16, 32, 12, -12, -24, 6, 26, -4, -18, -44, -26, -28, 10, -36, 2, 44, -14, -24, -38, 40, 38, 42, 44, -16, -14, -12, -8, 6, -12, -10, 34, -2, -4, 4, 6, -10, 32, -48, 14, 4, 8, -24, 38, -22, 2, -18, -28, 22, 26, -4, 30, 16, 28, -50, 24, -10, 42, 12, 32, -18, 50, 4, -8, -4, -16, -16, 50, 42, 6, -12, -54, 16, -36, -30, 24, -40, -26], "trace_hash": 1588924079463638771, "simple": true, "squarefree": true, "power": true, "conductor": [[2, 4], [3, 1]], "log_conductor": {"__RealLiteral__": 0, "data": "3.87120101090789092906", "prec": 74}, "q_gonality": 2, "q_gonality_bounds": [2, 2], "qbar_gonality": 2, "qbar_gonality_bounds": [2, 2], "bad_primes": [2, 3], "num_bad_primes": 2, "level_radical": 6, "level_is_squarefree": false, "cm_discriminants": [], "obstructions": [], "pointless": false, "num_known_degree1_points": 3, "lattice_labels": ["1.1.0.a.1", "3.4.0.a.1", "4.2.0.a.1", "4.4.0.a.1", "4.8.0.b.1", "12.8.0.a.1", "12.16.0.b.1", "12.16.1.a.1", "12.32.1.b.1", "12.64.1.b.1"], "lattice_x": [5304, 2534, 5304, 8412, 6487, 2669, 912, 4628, 4155, 2770], "curve_label": "48.a4", "canonical_conjugator": [5, 9, 4, 7], "has_obstruction": -1, "num_known_degree1_noncusp_points": 2, "num_known_degree1_noncm_points": 2, "models": 1, "all_degree1_points_known": null}